1 / 15

DRILL Prove each pair of triangles are congruent.

DRILL Prove each pair of triangles are congruent. Given: PQ is congruent to QR and PS is congruent to SR. Given: AB ║ CD, BC ║ DA. Objectives:. Use congruent triangles to plan and write proofs. Use congruent triangles to prove constructions are valid.

xylia
Download Presentation

DRILL Prove each pair of triangles are congruent.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. DRILLProve each pair of triangles are congruent. Given: PQ is congruent to QR and PS is congruent to SR. Given: AB ║ CD, BC ║ DA

  2. Objectives: • Use congruent triangles to plan and write proofs. • Use congruent triangles to prove constructions are valid.

  3. 8.4 Using Triangle CongruenceCPCTC

  4. B F That means that EG CB A E What is AC congruent to? G C Corresponding parts • When you use a shortcut (SSS, AAS, SAS, ASA, HL) to show that 2 triangles are congruent, that means that ALL the corresponding parts are congruent. Segment FE

  5. Corresponding parts of congruent triangles are congruent. Corresponding parts of congruent triangles are congruent. Corresponding parts of congruent triangles are congruent. Corresponding parts of congruent triangles are congruent.

  6. Corresponding Parts of Congruent Triangles are Congruent. CPCTC You can only useCPCTCin a proofAFTERyou have proved congruence.

  7. Given: A is the midpoint of MT, A is the midpoint of SR. Prove: NS is congruent to TR. Ex. Proof

  8. Statements: A is the midpoint of MT, A is the midpoint of SR. MA ≅ TA, SA ≅ RA MAS ≅ TAR ∆MAS ≅ ∆TAR NS is congruent to TR Reasons: Given Given: A is the midpoint of MT, A is themidpoint of SR.Prove: NS is congruent to TR.

  9. Statements: A is the midpoint of MT, A is the midpoint of SR. MA ≅ TA, SA ≅ RA MAS ≅ TAR ∆MAS ≅ ∆TAR NS is congruent to TR Reasons: Given Definition of a midpoint Given: A is the midpoint of MT, A is themidpoint of SR.Prove: NS is congruent to TR.

  10. Statements: A is the midpoint of MT, A is the midpoint of SR. MA ≅ TA, SA ≅ RA MAS ≅ TAR ∆MAS ≅ ∆TAR NS is congruent to TR Reasons: Given Definition of a midpoint Vertical Angles Theorem Given: A is the midpoint of MT, A is themidpoint of SR.Prove: NS is congruent to TR.

  11. Statements: A is the midpoint of MT, A is the midpoint of SR. MA ≅ TA, SA ≅ RA MAS ≅ TAR ∆MAS ≅ ∆TAR NS is congruent to TR Reasons: Given Definition of a midpoint Vertical Angles Theorem SAS Congruence Postulate Given: A is the midpoint of MT, A is themidpoint of SR.Prove: NS is congruent to TR.

  12. Statements: A is the midpoint of MT, A is the midpoint of SR. MA ≅ TA, SA ≅ RA MAS ≅ TAR ∆MAS ≅ ∆TAR NS is congruent to TR Reasons: Given Definition of a midpoint Vertical Angles Theorem SAS Congruence Postulate CPCTC Given: A is the midpoint of MT, A is themidpoint of SR.Prove: NS is congruent to TR.

  13. Given: 1≅2, 3≅4. Prove ∆BCE≅∆DCE Prove: segment DC is congruent to segment CD Ex. 2: Using more than one pair of triangles. 2 4 3 1

  14. Statements: QS  RP PT ≅ RT Reasons: Given Given Given: QSRP, segment PT≅ segment RTProve: segment PS≅ segment RS 4 3 1

  15. Homework • Page 429 • #’s 1 – 10 and #12

More Related